Quantum correlations are unique. On the one hand, they are stronger than those produced by any local hidden variables model. On the other hand, stronger-than-quantum correlations exist which are nevertheless non-signaling. It is therefore customarily believed that Nature is not more nonlocal than predicted by quantum mechanics due to some principle other than relativistic causality.In this talk I will prove that in an inherently indeterministic theory, relativistic causality does lead to strict bounds on quantum mechanical correlations. Without assuming quantum mechanics, I will discussa general consequence of relativistic causality under indeterminism, named relativistic independence [1].I will show that it induces a particular statistical structure, which gives rise to the state-of-the-art bounds on bipartite quantum correlations, as well as to a few tighter bounds. Moreover, relativistic independence holds in general multipartite scenarios which leads to further bounds. These results show that theories with correlations stronger than quantum do not satisfy the relativistic independence property and are therefore incompatible with either indeterminism (in the sense of this work) or relativistic causality. Quantum mechanics employs specific uncertainty relations for preventing a clash between causality and nonlocality [2]. I will then characterize and restrict all possible models for nonlocal hidden variables [3]. Finally, I will describe an upcoming series of experiments in Ottawa which I designed for testing theabove results. These experiments are based on my previous demonstration of sequential and protective measurements with the Turin group [4,5].